def test_intervals_intersection(self):
nullx = NullInterval(x)
# All nulls
assert nullx.intersection(nullx) == nullx
nully = NullInterval(y)
ix = Interval(x, -2, 2)
iy = Interval(y, -2, 2)
# Mixed nulls and defined
assert nullx.intersection(ix) == nullx
assert nullx.intersection(iy) == nullx
assert nullx.intersection(iy) != nully
assert nully.intersection(iy) == nully
ix2 = Interval(x, -8, -3)
ix3 = Interval(x, 3, 4)
# All defined disjoint
assert ix.intersection(ix2) == nullx
assert ix.intersection(ix3) == nullx
assert ix2.intersection(ix3) == nullx
assert ix.intersection(iy) == nullx
assert iy.intersection(ix) == nully
ix4 = Interval(x, 1, 4)
ix5 = Interval(x, -3, 0)
# All defined overlapping
assert ix.intersection(ix4) == Interval(x, 1, 2)
assert ix.intersection(ix5) == Interval(x, -2, 0)
def test_intervals_subtract(self):
nullx = NullInterval(x)
# All nulls
assert nullx.subtract(nullx) == nullx
ix = Interval(x, 2, -2)
# Mixed nulls and defined on the same dimension
assert nullx.subtract(ix) == nullx
assert ix.subtract(ix) == Interval(x, 0, 0)
assert ix.subtract(nullx) == ix
ix2 = Interval(x, 4, -4)
ix3 = Interval(x, 6, -6)
# All defined same dimension
assert ix2.subtract(ix) == ix
assert ix.subtract(ix2) == Interval(x, -2, 2)
assert ix3.subtract(ix) == ix2
def test_intervals_merge(self):
nullx = NullInterval(x)
# All nulls
assert nullx.merge(nullx) == nullx
ix = Interval(x, -2, 2)
# Mixed nulls and defined on the same dimension
assert nullx.merge(ix) == ix
assert ix.merge(ix) == ix
assert ix.merge(nullx) == ix
ix2 = Interval(x, 1, 4)
ix3 = Interval(x, -3, 6)
# All defined overlapping
assert ix.merge(ix2) == Interval(x, -2, 4)
assert ix.merge(ix3) == ix3
assert ix2.merge(ix3) == ix3
ix4 = Interval(x, 0, 0)
ix5 = Interval(x, -1, -1)
ix6 = Interval(x, 9, 11)
# Non-overlapping
assert ix.merge(ix4) == Interval(x, -2, 2)
assert ix.merge(ix5) == Interval(x, -2, 2)
assert ix4.merge(ix5) == Interval(x, -1, 0)
assert ix.merge(ix6) == Interval(x, -2, 11)
assert ix6.merge(ix) == Interval(x, -2, 11)
assert ix5.merge(ix6) == Interval(x, -1, 11)
def test_intervals_union(self):
nullx = NullInterval(x)
# All nulls
assert nullx.union(nullx) == nullx
ix = Interval(x, -2, 2)
# Mixed nulls and defined on the same dimension
assert nullx.union(ix) == ix
assert ix.union(ix) == ix
assert ix.union(nullx) == ix
ix2 = Interval(x, 1, 4)
ix3 = Interval(x, -3, 6)
# All defined overlapping
assert ix.union(ix2) == Interval(x, -2, 4)
assert ix.union(ix3) == ix3
assert ix2.union(ix3) == ix3
ix4 = Interval(x, 4, 8)
ix5 = Interval(x, -3, -3)
ix6 = Interval(x, -10, -3)
nully = NullInterval(y)
iy = Interval(y, -2, 2)
# Mixed disjoint (note: IntervalGroup input order is relevant)
assert ix.union(ix4) == IntervalGroup([ix, ix4])
assert ix.union(ix5) == Interval(x, -3, 2)
assert ix6.union(ix) == IntervalGroup([ix6, ix])
assert ix.union(nully) == IntervalGroup([ix, nully])
assert ix.union(iy) == IntervalGroup([ix, iy])
assert iy.union(ix) == IntervalGroup([iy, ix])
def test_intervals_subtract(self, x, y):
nullx = NullInterval(x)
# All nulls
assert nullx.subtract(nullx) == nullx
ix = Interval(x, 2, -2)
# Mixed nulls and defined on the same dimension
assert nullx.subtract(ix) == nullx
assert ix.subtract(ix) == Interval(x, 0, 0)
assert ix.subtract(nullx) == ix
ix2 = Interval(x, 4, -4)
ix3 = Interval(x, 6, -6)
# All defined same dimension
assert ix2.subtract(ix) == ix
assert ix.subtract(ix2) == Interval(x, -2, 2)
assert ix3.subtract(ix) == ix2
c = Constant(name='c')
ix4 = Interval(x, c + 2, c + 4)
ix5 = Interval(x, c + 1, c + 5)
# All defined symbolic
assert ix4.subtract(ix5) == Interval(x, 1, -1)
assert ix5.subtract(ix4) == Interval(x, -1, 1)
assert ix5.subtract(ix) == Interval(x, c - 1, c + 7)
def test_intervals_union(self, x, y):
nullx = NullInterval(x)
# All nulls
assert nullx.union(nullx) == nullx
ix = Interval(x, -2, 2)
# Mixed nulls and defined
assert nullx.union(ix) == ix
assert ix.union(ix) == ix
assert ix.union(nullx) == ix
ix2 = Interval(x, 1, 4)
ix3 = Interval(x, -3, 6)
assert ix.union(ix2) == Interval(x, -2, 4)
assert ix.union(ix3) == ix3
assert ix2.union(ix3) == ix3
ix4 = Interval(x, 4, 8)
ix5 = Interval(x, -3, -3)
ix6 = Interval(x, -10, -3)
nully = NullInterval(y)
iy = Interval(y, -2, 2)
assert ix.union(ix4) == Interval(x, -2, 8)
assert ix.union(ix5) == Interval(x, -3, 2)
assert ix6.union(ix) == Interval(x, -10, 2)
# The union of non-compatible Intervals isn't possible, and an exception
# is expected
ixs1 = Interval(x, -2, 2, stamp=1)
for i, j in [(ix, nully), (ix, iy), (iy, ix), (ix, ixs1), (ixs1, ix)]:
try:
i.union(j)
assert False # Shouldn't arrive here
except ValueError:
assert True
except:
# No other types of exception expected
assert False
# Mixed symbolic and non-symbolic
c = Constant(name='c')
ix7 = Interval(x, c, c + 4)
ix8 = Interval(x, c - 1, c + 5)
assert ix7.union(ix8) == Interval(x, c - 1, c + 5)
assert ix8.union(ix7) == Interval(x, c - 1, c + 5)
# Symbolic with properties
s = Scalar(name='s', nonnegative=True)
ix9 = Interval(x, s - 2, s + 2)
ix10 = Interval(x, s - 1, s + 1)
assert ix.union(ix9) == Interval(x, -2, s + 2)
assert ix9.union(ix) == Interval(x, -2, s + 2)
assert ix9.union(ix10) == ix9
assert ix10.union(ix9) == ix9
def test_intervals_intersection(self, x, y):
nullx = NullInterval(x)
# All nulls
assert nullx.intersection(nullx) == nullx
nully = NullInterval(y)
ix = Interval(x, -2, 2)
iy = Interval(y, -2, 2)
# Mixed nulls and defined
assert nullx.intersection(ix) == nullx
assert nullx.intersection(iy) == nullx
assert nullx.intersection(iy) != nully
assert nully.intersection(iy) == nully
ix2 = Interval(x, -8, -3)
ix3 = Interval(x, 3, 4)
assert ix.intersection(ix2) == Interval(x, -2, -3)
assert ix.intersection(ix3) == Interval(x, 3, 2)
assert ix2.intersection(ix3) == Interval(x, 3, -3)
assert ix.intersection(iy) == nullx
assert iy.intersection(ix) == nully
ix4 = Interval(x, 1, 4)
ix5 = Interval(x, -3, 0)
assert ix.intersection(ix4) == Interval(x, 1, 2)
assert ix.intersection(ix5) == Interval(x, -2, 0)
# Mixed symbolic and non-symbolic
c = Constant(name='c')
ix6 = Interval(x, c, c + 4)
ix7 = Interval(x, c - 1, c + 5)
assert ix6.intersection(ix7) == Interval(x, c, c + 4)
assert ix7.intersection(ix6) == Interval(x, c, c + 4)
# Symbolic with properties
s = Scalar(name='s', nonnegative=True)
ix8 = Interval(x, s - 2, s + 2)
ix9 = Interval(x, s - 1, s + 1)
assert ix.intersection(ix8) == Interval(x, s - 2, 2)
assert ix8.intersection(ix) == Interval(x, s - 2, 2)
assert ix8.intersection(ix9) == Interval(x, s - 1, s + 1)
assert ix9.intersection(ix8) == Interval(x, s - 1, s + 1)